How to approach this handwritten digit recognition?
I think one approach you can try to segment the digits and Connected Components Labeling (https://en.wikipedia.org/wiki/Connected-component_labeling).
With it, you'll end up with a label for each letter and then you can try to find the convex hull of the letter.
After that, just crop a square for each convex hull and input it to your CNN.
Notice that it will only if there is at least one pixel between the letters...